The word is - linn. I thought it meant 'with us', but I've found it being used in a completely different way. In the NCCA document Eolas do mhúinteoirí about Gaeilge neamhfhoirmiúil it's used in these sentences.
Dhá ghné atá le breithniú anseo: úsáid na Gaeilge neamhfhoirmiúla le linn an cheachta Ghaeilge, agus lasmuigh de.
Two main aspects of Gaeilge neamhfhoirmiúla to consider are informal language use within, and outside of, the formal language lesson.
(I must just add that this is something I completely agree with - but please don't tell the French educational establishment I said so, will you?)
Úsáid na Gaeilge le linn an cheachta Ghaeilge. Úsáid na Gaeilge le linn an lae scoile.
I see that in Pota Focal it means during, but is it a special use of le or is it a word in its own right?

In this case, linn is a noun meaning "space of time, period". Hence, le linn ruda for the space of time of sth", i.e., "during/in the course of sth".

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Well I'm glad you told me that because once again it isn't in the dictionary, or if it is, it isn't explained.
GRMA
PS couldn't they say - i rith?

Aye, you could say le linn, i rith, i gcaitheamh, ar feadh...

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

I rith is a bit more stringent about requiring a unit or measurement of time to follow it; le linn can take just about any noun phrase that somehow contains a space of time. Le linn an rialtais seo, for example, means ‘during the time this government is in place’; i rith an rialtais seo doesn’t really make sense—it means ‘during this government’.

I rith also more specifically means ‘during the course of X’, whereas le linn also means ‘while X lasts/lasted’ or ‘for the duration of X’ or ‘at some point in the duration of X’. They’re often synonymous, but sometimes minor differences can make one sound odd.

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Not a native speaker.

Always wait for at least three people to agree on a translation, especially if it’s for something permanent.

My translations are usually GU (Ulster Irish), unless CO (Standard Orthography) is requested.

It is in the dictionary (FGB), Franc, and of course it is explained - although it has a number of meanings.

Bhuel, Scooby, a chara - there's just one slight problem there - I haven't got it, but when I grow up and get bigger, I'm going to get one like that. I even had a birthday last week when I was all of 16 years old (there's somebody looking over my shoulder at the moment, poking me in the ribs and telling me that I should be ashamed of myself and that I should be putting those two numbers the other way round and why haven't I got a carte bleue - but I haven't got one of those either - the dictionary I have is the Collins and whatever else you can find on the net)

Caithfidh tú litir a scríobh chuig Daidí na Nollag, láithreach. Chuala mé go bhfuil gach rud ina mhála mór....má tá tú go maith.

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